Having just looked at this topic.
In addition to the link I would add
Rate is defined as change of concentration divided by time
The rate equation looks a bit like equilibrium constant equation because of the concentration terms - don't be deceived - they are significantly different expressions
The equlibrium equation includes concentrations of reactants and products.
The rate equation only includes concentration of REACTANTS - repeat many times
The rate equation powers of concentration of REACTANTS - are not connected with the number of moles of reactant in balanced equation - repeat many times
Most questions are provide data on INITIAL rate and INITIAL concentration of reactants - and then vary the concentration of one species - so you can determine the rate order of each species.
The curves are in two groups
Curve type 1: Concentration of reactant versus time
Curve type 2: Rate versus (initial) concentration of reactant
Don't mix the graph types up. Learn the shapes and be able to explain for NO REACTION (rarely given), zero order, first order, second order for both graph types.
Rate half-life is easiest to understand on the first-order concentration - time graph. Then extend from there to other orders.
With a little bit of "head maths" and some thinking, you should be able to relate the shape of a concentration-time graph to the rate-concentration graph for each order. Remember rate = - gradient of the concentration-time graph
Clive